Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

Page concordance

< >
Scan Original
121 109
122 110
123 111
124 112
125 113
126 114
127 115
128 116
129 117
130 118
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
141 129
142 130
143 131
144 132
145 133
146 134
147 135
148 136
149 137
150 138
< >
page |< < (37) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div7" type="chapter" level="2" n="1">
            <div xml:id="echoid-div117" type="math:theorem" level="3" n="57">
              <p>
                <s xml:id="echoid-s505" xml:space="preserve">
                  <pb o="37" rhead="THEOREM. ARITH." n="49" file="0049" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0049"/>
                g. in
                  <var>.g.h</var>
                . </s>
                <s xml:id="echoid-s506" xml:space="preserve">Nunc ex ſpeculatione præcedentis theorematis, eadem erit proportio
                  <var>.n.
                    <lb/>
                  t.</var>
                ad
                  <var>.o.u.</var>
                quæ eſt
                  <var>.n.s.</var>
                ad
                  <var>.o.r.</var>
                </s>
                <s xml:id="echoid-s507" xml:space="preserve">quare pro-
                  <lb/>
                ductum
                  <var>.k.</var>
                ex definitione ſimile erit
                  <lb/>
                  <figure xlink:label="fig-0049-01" xlink:href="fig-0049-01a" number="66">
                    <image file="0049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0049-01"/>
                  </figure>
                producto
                  <var>.m.</var>
                cum vtraque ſint rectan-
                  <lb/>
                gula, vnde proportio
                  <var>.k.</var>
                ad
                  <var>.m.</var>
                ad pro-
                  <lb/>
                portionem
                  <var>.n.t.</var>
                ad
                  <var>.o.u.</var>
                ex .18. ſexti du-
                  <lb/>
                pla erit. </s>
                <s xml:id="echoid-s508" xml:space="preserve">Igitur proportio
                  <var>.k.</var>
                ad
                  <var>.m.</var>
                æ-
                  <lb/>
                qualis erit proportioni
                  <var>.x.</var>
                ad
                  <var>.y.</var>
                et
                  <var>.p.</var>
                  <lb/>
                ad
                  <var>.q.</var>
                et
                  <var>.i.</var>
                ad
                  <var>.l.</var>
                & permutando ſic ſe ha-
                  <lb/>
                bebit
                  <var>.k.</var>
                ad
                  <var>.i.</var>
                ſicut
                  <var>.m.</var>
                ad
                  <var>.l.</var>
                ſed
                  <var>.x.p.</var>
                ad
                  <var>.i.</var>
                  <lb/>
                ſicſe habere probatum eſt vt
                  <var>.y.q.</var>
                ad
                  <var>.l</var>
                .
                  <lb/>
                </s>
                <s xml:id="echoid-s509" xml:space="preserve">Quare ex eadem .24. quinti ſic ſe habe
                  <lb/>
                bit
                  <var>.x.p.k.</var>
                ad
                  <var>.i.</var>
                ſicut
                  <var>.y.q.m.</var>
                ad
                  <var>.l.</var>
                ſed
                  <var>.y.q.
                    <lb/>
                  m.</var>
                æqualis eſt
                  <var>.l</var>
                . </s>
                <s xml:id="echoid-s510" xml:space="preserve">Itaque
                  <var>.x.p.k.</var>
                pariter
                  <var>.i.</var>
                  <lb/>
                æqualis erit.</s>
              </p>
            </div>
            <div xml:id="echoid-div119" type="math:theorem" level="3" n="58">
              <head xml:id="echoid-head74" xml:space="preserve">THEOREMA
                <num value="58">LVIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s511" xml:space="preserve">ALIVD quoque problema, nec tamen definitum, veteres propoſuerunt,
                  <lb/>
                nempe an aliquis numerus in .4. eiuſmodi partes diuidi poſſit, vt ſumma qua-
                  <lb/>
                dratorum duarum partium dupla ſit ſummæ quadratorum reliquarum duarum.</s>
              </p>
              <p>
                <s xml:id="echoid-s512" xml:space="preserve">Verum huius effectio & ſpeculatio non erit difficilis,
                  <reg norm="cum" type="context">cũ</reg>
                ſit eadem quæ præmiſsis
                  <lb/>
                proximè duobus theorematibus allata fuit, ſumpta nempe ſumma radicum quarun
                  <lb/>
                cunque ſic ſe habentium, prout dictum fuit. </s>
                <s xml:id="echoid-s513" xml:space="preserve">Verbigratia .44. cuius partes erunt.
                  <lb/>
                16. 12. 14. 2.
                  <reg norm="tunc" type="context">tũc</reg>
                progrediemur regula de tribus dicentes. </s>
                <s xml:id="echoid-s514" xml:space="preserve">Si .44 numerum propoſi-
                  <lb/>
                tum valet, quid .16. pars maior? </s>
                <s xml:id="echoid-s515" xml:space="preserve">nempe valebit partem maiorem numeri propoſi-
                  <lb/>
                ti reſpondentem .16. idem de cæteris dico.</s>
              </p>
              <p>
                <s xml:id="echoid-s516" xml:space="preserve">Porrò ſpeculatio eadem eſt cum ſuperioribus.</s>
              </p>
            </div>
            <div xml:id="echoid-div120" type="math:theorem" level="3" n="59">
              <head xml:id="echoid-head75" xml:space="preserve">THEOREMA
                <num value="59">LIX</num>
              .</head>
              <p>
                <s xml:id="echoid-s517" xml:space="preserve">CVR diuidens propoſitum numerum in duas eiuſmodi partes, vt productum
                  <lb/>
                radicum quadratarum ipſarum partium æquale ſit alteri numero propoſito,
                  <lb/>
                cuius
                  <reg norm="tamen" type="context">tamẽ</reg>
                quadratum maius
                  <reg norm="non" type="context">nõ</reg>
                ſit quadrato dimidij primi numeri propoſiti. </s>
                <s xml:id="echoid-s518" xml:space="preserve">Rectè
                  <lb/>
                ſecundum numerum propoſitum in ſeipſum multiplicat, &
                  <reg norm="eundem" type="context">eundẽ</reg>
                ex quadrato di-
                  <lb/>
                midij primi detrahit,
                  <reg norm="reſiduique" type="simple">reſiduiq́;</reg>
                quadratam radicem ſubtrahit ex dimidio ipſius pri-
                  <lb/>
                mi, ex quo datur minor pars quæſita, quaipſi dimidio coniuncta, maior pars ha-
                  <lb/>
                betur.</s>
              </p>
              <p>
                <s xml:id="echoid-s519" xml:space="preserve">Exempli gratia, ſi proponatur numerus, 20. propoſito modo, in duas partes
                  <lb/>
                eiuſmodi diuidendus, vt productum radicum æquale ſit (verbigratia) 8. </s>
                <s xml:id="echoid-s520" xml:space="preserve">Dimi-
                  <lb/>
                dium priminumeri in ſeipſum multiplicabimus, cuius quadratum erit .100. ex
                  <lb/>
                quo quadratum ſecundi numeri, nempe .64. detrahemus,
                  <reg norm="remanebitque" type="simple">remanebitq́;</reg>
                .36. cuius radi
                  <lb/>
                ce quadrata coniuncta .10. dimidio inquam primi numeri propoſiti, dabitur nume
                  <lb/>
                rus .16. pars maior, & ſubtracta à dimidio, dabitur minor pars, nempe .4.</s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum